The gene for colour has space for two alleles. It can have two yellow base alleles (homozygous), two white base alleles (also homozygous), or one white base allele and one yellow base allele (heterozygous). When both different alleles are present, only the yellow base trait is expressed since it is dominant over the white base allele. Two yellow base alleles equal a yellow based bird. One yellow base and one white base allele equal a yellow based bird. Two white base alleles equal a white based bird. If there were other body colours, they might be dominant to yellow base, or recessive to yellow base but dominant to white base. Either way, if an allele is recessive, it will never show up in the presence of a dominant allele in a heterozygous individual.
But all that only applies to simple dominance and recessive inheritance. There is also semi-dominance, co-dominance, incomplete dominance, and multiple alleles. With semi-dominance, traits will only show up in the presence of other traits. With co-dominance, two traits are expressed at the same time (a white flower plus a red flower equals a flower with splotches of red and white on it). With incomplete dominance, traits are mixed (a red flower plus a blue flower equals a purple flower). Multiple alleles are when a trait being expressed is due to the combination of many genes and alleles working together (like eye colour).
A lot of the mutations found in budgies are examples of simple dominant-recessive inheritance, but some are also examples semi, co and incomplete dominance; body colour just doesn't happen to be one of them.